The document is a mathematics lecture on integers. It discusses the four integer operations of addition, subtraction, multiplication, and division. It provides examples of how to perform each operation on integers and the rules for determining if the result is positive or negative. Addition and subtraction are explained using rules about combining positive and negative integers. Multiplication and division are covered together, as their rules are the same - the result is positive if the signs are the same and negative if the signs are different.
3. The coldest continent on Earth
is Antarctica where average
temperature range from 5°C in
summer to -80°C in winter. The
highest temperature ever
recorded in Antarctica was
15°C, while the lowest
temperature ever recorded in
Antarctica was -89.2°C.
4. In previous classes,
we have learnt about
whole numbers,
decimals and
fractions, such as 0,
9, 5.8 and
𝟏
𝟑
.
6. Negative Numbers:
Numbers that are
less than 0 are called
‘negative numbers’.
Such as -100, -1.1, -
𝟏
𝟖
0
-1
-2
-3
-4
-5
-6
7. Use of Negative Numbers
in the Real World
Negative Numbers Are Used to
Measure Temperature
8. Negative Numbers Are Used to
Measure Under Sea Level
0
10
20
30
-10
-20
-30
-40
-50
9. Negative Numbers Are Used to
Show Debt
Let’s say your parents bought a
car, but had to get a loan from
the bank for Rs.50,000.
How can we represent the amount
of money your parents have as an
integer?
-Rs.50,000
42. Rule #1 for
Adding Integers (+)
• The sum of two positive integers is
always positive.
5 + 1 = 6
43. Rule #2 for
Adding Integers (+)
• The sum of two negative integers is
always negative.
-5 + (-1) = -6
44. Rule #3 for
Adding Integers (+)
• The sum of a positive and a negative
integer could be positive, negative, or
zero.
45. Rule #3 for Adding
Integers Continued
• When you add a positive and negative
integer, you are really subtracting. Then,
you give the answer the sign of the
greater absolute value.
5 + (-1) = -4
-5 + 1 = 4
-5 + (-5) = 0
48. Rules for
Subtracting Integers (-)
• To subtract an integer, add its
opposite.
• You will need to correctly change all
subtraction problems into addition
problems!
50. There are three steps:
1. Keep the first integer the same.
(Same)
2. Change the subtraction sign into an
addition sign. (Change)
3. Take the opposite of the number
that immediately follows the newly
placed addition sign. (Change)
57. Rules for
Multiplying Integers (x)
• The product of two integers with the
same signs is POSITIVE.
• The product of two integers with
different signs is NEGATIVE.
58. Rules Summary for
Multiplication
• Positive x Positive = Positive
• Negative x Negative = Positive
• Positive x Negative= Negative
• Negative x Positive = Negative
63. • The rules for division are exactly
the same as those for multiplication.
• If we were to take the rules for
multiplication and change the
multiplication signs to division signs,
we would have an accurate set of
rules for division.
64. Rules for
Dividing Integers (÷)
• The quotient of two integers with
the same signs is POSITIVE.
• The quotient of two integers with
different signs is NEGATIVE.
71. ANSWER
• The sum of two positive integers is always
positive.
• The sum of two negative integers is always
negative.
• When you add a positive and negative
integer, you are really subtracting. Then, you
give the answer the sign of the greater
absolute value.
77. ANSWER
• If the signs are the same, your answer is
always positive.
• If the signs are different, your answer is
always negative.
*Multiplication and Division Rules are the
same!
